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A gutsy birdie-birdie finish was not enough to put Tiger Woods through to the weekend at the US Open, but the US superstar "absolutely" believes he will win another major title.

Woods, playing the US Open for the first since he missed the cut in an injury-plagued 2015, was clearly heading for an early exit after a bogey at his 15th hole - the par-four sixth - pushed him to 12-over for the tournament.

Woods dug in and rolled in a 10-foot birdie putt at the eighth and a 17-footer at nine to complete a two-over par 72 for a 10-over total of 150 - still not enough to make the cut that fell at eight-over par.

"I'm not very happy the way I played and the way I putted," said Woods, who had been eyeing a round in the 60s after his opening 78.

"I'm 10-over par. So I don't know that you can be too happy and too excited about 10-over par."

But Woods, who was 14 shots behind leader Dustin Johnson, said that 10 official starts into his latest injury comeback he had no doubt he would add to his total of 14 major championships.

Woods, 10 years removed from his most recent major victory at the 2008 US Open, has shown flashes of brilliance in his latest comeback season but has yet to bring together every aspect of his game in one week to achieve a victory.

He finished second at the Valspar Championship in March and tied for fifth at the Arnold Palmer Invitational.

He put on a ball-striking clinic at the Memorial two weeks ago, but after putting his name atop the leaderboard in the third round succumbed to putting woes to finish tied for 23rd.

"I'm hitting it just fine," Woods added. "I just have not made any putts, and then, importantly, I haven't made those key ones to keep the momentum going, or if I have any positive momentum, I miss a putt and derail it."

Woods, 14 shots off world No 1 Dustin Johnson's tournament lead, can point to Shinnecock's par-four first as a key culprit in a disappointing US Open.

He opened the tournament with a triple bogey there on Thursday, and took double bogey there on Friday to open his second nine holes, after playing his first nine in even par.

He found the fairway off the tee, but his second shot landed in deep, rain-soaked rough. His third shot rolled through the green and his pitch left him 14 feet - from where he two-putted.

Dustin Johnson seems to be the man to beat at the US Open this year. Brad Penner / Reuters

Going the wrong way

A bogey at the second followed, and the bogey at the sixth before his bravura finish.

"I wanted to shoot something around 68, 67," Woods said. "I thought that would have been a great score.

"I looked at it as kind of progressively putting myself back into position. Unfortunately, I went the other way."

Woods has not made the cut at the US Open since 2013. After an early exit in 2015 he missed the next two editions.

He has not finished in the top five of a major since the 2013 Masters.

"I think they're all hard," Woods said of the grand slam events - and which he might be most likely to win again. "They're the hardest fields and usually the hardest setups. You have to be on."